Systems and methods for determining bids for placing advertisements

ABSTRACT

Systems, apparatuses, and methods are provided for determining a bid value for placing an advertisement onto advertising space available through an electronic marketplace. A method is used for calculating the option value of maintaining the advertisement in the advertising space during one or more periods of time. The option value may be based on expected profits and the estimated future value of maintaining the advertisement. The option value may then be used to calculate the bid price for placing the advertisement.

FIELD OF THE INVENTION

Principles consistent with embodiments of the present invention relateto facilitating the interaction of parties engaged in electronic markettransactions, and more specifically, to calculating a bid price foradvertising space available on an electronic medium.

BACKGROUND OF THE INVENTION

Since the early 1990's, the number of people using the World Wide Webhas grown at a substantial rate. As more users take advantage of theWorld Wide Web, higher volumes of traffic are generated over theInternet. Because the benefits of commercializing the Internet to takeadvantage of these higher traffic volumes can be tremendous, businessesincreasingly seek means to advertise their products or services on-line.These advertisements may appear, for example, in the form of leasedadvertising space (e.g., “banners”) on websites or as advertisementspresented to digital television users, which are comparable to rentedbillboard space or to commercials broadcasted during television or radioprograms.

When a company advertises on a website, it may benefit from the volumeof advertisements or impressions that it places on the website, thenumber of users that select or “click” on each advertisement, and thenumber of sales or other “conversions” that result from each display ofan advertisement. Each instance that an advertisement is placed on a webpage may be referred to as an “impression.” Companies may pay perimpression, per click, and/or per conversion, regardless of whether ornot the action for which they are paying (e.g., impressions, clicks,etc.) is the action that benefits them. Therefore, in addition towanting to predict impressions, clicks, and conversions, a company maywant to determine a bid price, which represents the highest price thatthe company is willing to pay for placing an advertisement on a website.The determination of a bid price may help companies, and those obtainingadvertising space on their behalf, to assess the potential benefit ofplacing a particular advertisement on a particular web page.Accordingly, companies have a need to determine bid prices for placingadvertisements on web pages.

It is accordingly an object to overcome the shortcomings of currenttechniques for pricing bids.

SUMMARY OF THE INVENTION

Certain embodiments of the present invention disclose methods fordetermining a bid price of an advertisement by dividing a time periodbeginning at an initial time into a set of learning periods associatedwith the advertisement and generating a set of expected revenue ratesfor the set of learning periods. A cost for placing the advertisement inthe learning period starting at the initial time is estimated and acurrent option value is determined based on the estimated cost. Thecurrent option value is determined by, for a final learning period inthe set of learning periods, determining a continuation valuerepresenting the expected profit over the final learning period and anoption value representing a value of the option to stop placing theadvertisement at the beginning of the final learning period. Startingwith a learning period just prior to the final learning period, acontinuation value is determined representing a value of continuing toplace the advertisement, the continuation value based on the expectedrevenue rate for the learning period and the continuation values oflater learning periods and an option value is determined representing avalue of the option to stop placing the advertisement at the beginningof the learning period, the option value based on the continuation valuefor the learning period. These steps are repeated for each priorlearning period until an option value is determined for the learningperiod starting at the initial time. A current option value equal to theoption value is determined for the learning period starting at theinitial time, and if the current option value is not zero, the estimatedcost is adjusted and the process is repeated. If the current optionvalue is zero, the bid price is set equal to the estimated cost andsubmitted to an advertising exchange that places online advertising.

In other embodiments, a method is disclosed for determining a bid priceof an advertisement by dividing a time period beginning at an initialtime into a set of learning periods associated with the advertisementand generating a set of possible expected revenue rates for eachlearning period in the set of learning periods. A cost for placing theadvertisement is estimated and a current option value for the initiallearning period is determined based on the estimated cost by recursivelydetermining, for each learning period beginning with a final learningperiod in the set of learning periods, a continuation value associatedwith the expected revenue rate for the learning period and thecontinuation values of later learning periods, and an option value,based on the continuation value, associated with an option to stopplacement of the advertisement in the learning period. Until the currentoption is zero, the estimated cost is adjusted and the determination isrepeated. When the current option value is zero, the bid price is setequal to the estimated cost and submitted to an advertising exchangethat places online advertising.

In still other embodiments of the invention, a bid calculating apparatusis disclosed for determining a bid price of an advertisement. The bidcalculating apparatus comprises a learning period module configured todivide a time period beginning at an initial time into a set of learningperiods associated with the advertisement. The bid calculating apparatusfurther comprises a lattice module configured to generate a set ofexpected revenue rates for each learning period in the set of learningperiods and determine a current option value for the initial learningperiod based on the estimated cost by recursively determining, for eachlearning period beginning with a final learning period in the set oflearning periods. This is done by determining a continuation valueassociated with the expected revenue rate for the learning period andthe continuation values of later learning periods, and an option value,based on the continuation value, associated with an option to stopplacement of the advertisement in the learning period. The bidcalculating apparatus further comprises a bid generator configured todetermine whether the current option value is zero, adjust the estimatedcost and direct the lattice module to repeat the determining function,when it is determined that the current option value is not zero, and setthe bid price equal to the estimated cost, when it is determined thatthe current option value is zero.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of a system that provides a marketplace foradvertising inventory, consistent with an embodiment of the presentinvention.

FIG. 2 shows a block diagram of an exemplary campaign optimizer formanaging advertising campaigns, consistent with an embodiment of thepresent invention.

FIGS. 3A-3B show an exemplary process for determining a bid based on anoption price consistent with an embodiment the present invention.

FIG. 4 shows an exemplary embodiment of a bid calculator consistent withan embodiment the present invention.

FIG. 5 shows an exemplary embodiment of a portion of a lattice structureconsistent with an embodiment of the present invention.

FIG. 6 shows an exemplary embodiment of a portion of a lattice structureconsistent with an embodiment of the present invention.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to exemplary embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

A company may determine a bid price using at least two elements. First,the company may calculate the bid price based on the short term profitthat it expects to receive when placing the advertisement on a web page.The expected short term profit due to placing an advertisement on a webpage may be calculated, for example, using the number of conversionsthat result after placing the advertisement. Determining short termprofits due to placing an advertisement may take into account additionalfactors, such as the time lag between a successful sale or conversionand the impression that resulted in the sale or conversion. Taking thetime lag into account when calculating conversions is discussed in U.S.Provisional patent application Ser. No. 11/819,058, entitled “AdaptiveLag Compensated Prediction of Future Success Rate” and filed on Jun. 25,2007, which is incorporated herein in its entirety by reference.

Second, a company may base its bid price on a learning value. Thelearning value represents the additional price that the company iswilling to pay to better estimate the expected revenue of maintainingthe advertisement on the web page. Although the company may not be ableto calculate the expected revenue with certainty, the additional datareceived by maintaining the advertisement on the web page may help thecompany to improve its expected revenue calculation. In some instances,a company may make trade-offs between the expected short term profit andthe learning value. For example, a company may accept short term lossesto learn if maintaining an advertisement on a web page may result infuture profits.

One problem with determining the bid price for placing an advertisementon a web page relates to determining of the learning value. For example,the learning value may lack a forward-looking component that takesfuture events into account when calculating the bid price. Instead ofusing a forward looking component, the learning value may be based onthe variance in revenue, but the revenue variance may be calculatedusing only revenue data collected during one or more previous timeperiods. Accordingly, using only prior event data such as the revenuevariance to calculate the learning value fails to take into accountfuture events that may also have an impact on the learning value. Forexample, as the end-of-life of the advertisement approaches, and theadvertisement is soon to be removed from the web page, the learningvalue of the bid price may be dramatically reduced. Embodimentsconsistent with the present invention, however, may be used to calculatea bid price that takes future events into account.

Consistent with certain embodiments, a process may be performed usingthese inputs and parameters:

Symbol Description r̆ Current estimate of the effective revenue rate perimpression. K₀ Variance of r̆. R Variance of the measurement noise perimpression. T Time remaining for a cell. μ Discount factor. δ Variancereduction parameter. γ Variance tolerance parameter. θ Bisectiontolerance parameterAdditional variable notations used in this document include:

Symbol Description c Cost rate per impression. N Number of learningperiods. Δ_(i) Length of learning period i. t_(i) Start time of learningperiod i. K_(i) Variance of the revenue rate at t_(i). r̆_(i) ^(j)Revenue rate scenario at time t_(j). p_(i) ^(j,k) Transition probabilityfrom r̆_(i) ^(j) to r̆_(i+1) ^(k). V_(i) ^(j) Option value scenario attime t_(j).

The effective revenue rate may represent an impression weighted averageof the revenue rates. A “cell” may correspond to a slot for placing aparticular advertisement at a particular place and time. For example, aslot for presenting a clickable internet advertisement for a discountbrokerage firm (the particular ad) on a Yahoo Finance client's internetbrowser (a particular network segment) may correspond to a cell. Animpression may occur when the advertisement is placed in a cell andpresented at the particular place and time. Each cell may be part of acampaign of cells—an advertising campaign. For example, an automobilecompany may launch a number of advertisements, each corresponding to oneor more cells, when it introduces a new car. The related advertisementsmay be part of the same campaign, and the cells related to theadvertisements may be “peers” of each other. Any number of campaigns maybe considered together in groups and the cells related to thosecampaigns may be considered peers of one another.

FIG. 1 shows a block diagram of a system for providing an electronicmarketplace for advertising inventory consistent with an embodiment ofthe present invention. Marketplace 100 may include advertiser 101,campaign optimizer 103, exchange 105, and publisher 107. Advertiser 101may have an advertising campaign and wish to purchase one or more cellson a web page to display the campaign advertisements. Further, as partof its advertising campaign, advertiser 101 may develop one or morecampaign goals 111. A campaign goal may describe one or more metrics,such as profitability and cost, that are to be maximized or minimizedduring the campaign. A campaign goal may include a list of deliveryterms for the campaign to indicate preferences and/or tolerances ofadvertiser 101. For example, advertiser 101 may include a delivery termto instruct that no more than $1,000 per month should be expended duringthe advertising campaign.

Advertiser 101 may send campaign goals 111 to campaign optimizer 103.Campaign optimizer 103 may use campaign goals 111 to formulate a biddingstrategy for the advertising campaign. For example, campaign optimizer103 may use campaign goals 111 to determine the web pages or types ofweb pages to target for placing advertisements. The group of targetedweb pages for an advertising campaign by advertiser 101 may be referredto as a target inventory. Bids 113 may identify the target inventory bylisting specific web pages and/or by describing the page characteristicsof the types of web pages on which advertiser 101 would like to placeadvertisements. The page characteristics may include, for example,statistics regarding the viewers of the web page and the number of timesthe web page is loaded. As part of the bidding process, campaignoptimizer 103 may repeatedly or continually submit bids 113 to exchange105. A bid 113 may describe the target inventory of web pages for theadvertising campaign as well as specify the maximum price peradvertising request and the maximum request volume that advertiser 101desires for the advertising campaign.

Publisher 107 may control inventory on one or more web pages that areavailable for displaying advertisements. Publisher 107 may send requests117 to exchange 105 to inform exchange 105 of the available inventory.Further, publisher 107 may maintain statistics and demographic dataregarding the web pages containing the available inventory. For example,publisher 107 may maintain statistics regarding the average number ofimpressions per hour, for each hour of the day, that were created in thepast week on a web page containing the available inventory.

Further, publisher 107 may maintain demographic data regarding the webpages containing the available inventory, demographic data that mayinclude, for example, the percentage of impressions created for peoplewithin specified age brackets, within certain geographic regions, orwithin defined income levels. Further, publisher 107 may include usageinformation within request 117, such as a base price for the inventoryon a web page, below which publisher 107 is unwilling to vend theinventory.

The usage information may also indicate an advertising period [0, T],which represents the period of time advertisements are to be placed inthe inventory. Further, in some embodiments, publisher 107 may indicatethat an advertisement may be removed from a web page before the end ofthe advertising period. Publisher 107 may provide the statistical,demographic, and usage data to exchange 105 as part of request 117.Additionally, the data from publisher 107 may be used by campaignoptimizer 103 to formulate future bids.

Exchange 105 facilitates the placement of advertisements from advertiser101 onto cells provided by publisher 107 by matching bids 113 withrequests 117. When request 117 for advertising space arrives frompublisher 107, exchange 105 may identify all bids 113 that have listedthe web page of request 117 within a target inventory. Exchange 105 maythen choose the winning bids that will receive at least some of theadvertising space offered by request 117. A manner in which exchange 105may choose the winning bid is described in co-pending U.S. patentapplication Ser. No. 11/984,244, entitled Systems and Methods forAllocating Electronic Advertising Opportunities and filed on Nov. 15,2007, which is incorporated herein by reference in its entirety.Exchange 105 may continuously receive requests 117 from publisher 107and match requests 117 to bids 113. Finally, exchange 105 may notifyadvertiser 101 and publisher 107 of the winning bids. Further, exchange105 may provide data 119 to campaign optimizer 103 and advertiser 101.For example, exchange 105 may include the demographic and statisticaldata received from publisher 107 as part of data 119.

FIG. 2 shows a block diagram of an exemplary campaign optimizer formanaging advertising campaigns consistent with an embodiment of thepresent invention. In the exemplary embodiment disclosed in FIG. 2 ,campaign optimizer 103 may include raw data aggregator 201, processcontrol 203, verified data storage 205, target discovery module 207,target evaluator 209, inventory target database 211, campaign manager213, and bid calculator 215. A skilled artisan will recognize that thecomponents of campaign optimizer 103 may be combined or separated inways other than the embodiment depicted in FIG. 2 . Further, in someembodiments, each of the components of campaign optimizer 103 may beincluded on the same electronic device. Alternatively, the components ofexemplary campaign optimizer 103 shown in FIG. 2 may be implemented ontwo or more electronic devices. Further, when multiple electronicdevices are used to implement campaign optimizer 103, the separateelectronic devices may be controlled by different entities. For example,in some embodiments, campaign manager 213 and bid calculator 215 may beimplemented on one electronic device controlled by advertiser 101 whilethe remaining components of campaign optimizer 103 may be implemented ona different electronic device controlled by a third party separate fromadvertiser 101 and publisher 107.

Raw data aggregator 201 accepts as input campaign goals 111 fromadvertiser 101 and data 119 from exchange 105. In addition, raw dataaggregator 201 may accept data from the Internet 250. In someembodiments, raw data aggregator 201 may accept a continuous data flowfrom any or all of advertiser 101, exchange 105, publisher 107, andInternet 250. Raw data aggregator 201 may use instructions received fromtarget discovery module 207 to parse and aggregate the received data.The instructions received from target discovery module 207 may identify,for example, the target web pages on which advertiser 101 may beinterested in placing advertisements. By parsing and aggregating thereceived data, raw data aggregator 201 may output to process control 203a collection of discrete-time signals containing data about the targetweb pages.

Process control 203 may be used to detect issues or problems withreceived data signals. Issues or problems that are left unattended mightseverely impact the ability of campaign optimizer 103 to bid onavailable advertising cells and to achieve campaign goals 111. Toprevent issues and problems from being left unattended, process control203 may be used to determine if a signal, such as a signal representingcampaign goals 111 and data 119, is behaving normally (i.e., is incontrol) or if the signal is exhibiting unusual behavior (i.e., is outof control). If a signal is out of control, then the ability of campaignoptimizer 103 to function properly may be affected. For example, ifproblems arise with the values in data 119 causing the related signal tobe out of control, then campaign optimizer 103 may calculate and submitbids requesting the wrong number of cells or with bid prices that aretoo high. Accordingly, process control 203 may be used to search forsignals that are out of control and warn those components of campaignoptimizer 103 that may be adversely effected.

Process control 203 may also be used to detect other failures in thereceived signals. When process control 203 detects a failure, then itmay take an appropriate preventative or corrective action. For example,process control 203 may prevent further bids 113 from being submittedwhen it detects a failure. If process control 203 has verified that asignal is in control, then it may process the data from the signal.Process control 203 may also pass the data to verified data storage 205.

Process control 203 may use the parsed data received from raw dataaggregator 201 to compute the effective revenue rate for a web page.Process control 203 may estimate the effective revenue rate, ř, as:

ř=Cρ,

where C represents the revenue per successful transaction (e.g. a sale)and ρ represents an estimate of the conversion rate of successfultransactions per impression. Accordingly, the effective revenue rate řmay have units of revenue per impression. As an example, process control203 may have calculated the revenue per successful transaction to be $50and the conversion rate to be 1 successful transaction for every 10,000impressions. In this example, the estimate of the effective revenuerate, ř, would equal $0.0050 per impression.

Process control 203 may use the captured raw data to determine thevariance, K₀, of the fundamental revenue rate. To do so, process control203 may set the variance to equal:

K ₀ =C ² Q

where Q equals the current estimate of the variance of ρ. As an example,process control 203 may have determined that the variance of ρ equals to0.000001. Keeping the revenue per successful transaction equal to $50,process control 203 may calculate the variance K₀ to equal 0.0025.

In certain embodiments, process control 203 may use the parsed data toestimate ř and K₀ by state space modeling and Kalman filtering. Thestate space model could be based on a model for the observed revenuerate per impression y for a period of time Δ such as:

y _(t+Δ) =r+v _(t,Δ)

where r equals the true, unknown revenue rate per impression and v_(t,Δ)represents the measurement noise at time t over the interval Δ. Kalmanfiltering may be used to compute ř and K₀, the estimate of rand itsvariance, respectively.

Process control 203 may use the parsed data to determine the measurementnoise for the observed revenue rate of a cell. The measurement noise maytake into account the volatility of the revenue observed for a set ofimpressions for a given revenue rate for a web page created over periodof time. Raw data aggregator 201 may calculate the variance of themeasurement noise, R, given the impressions and the estimated revenuerate. In some embodiments, the value of the variance of the measurementnoise may equal:

$R = \frac{C\overset{\hat{}}{r}}{\eta_{a}}$

In this equation, η_(a) may represent the set of available impressionsfor the web page for a given advertiser for a unit of time.

Process control 203 may use the parsed data to determine a discountfactor for the future expected revenue. Process control 203 maycalculate the discount factor, μ, based on a combination of a risklessinterest rate and a hazard rate associated with the advertisement beingprematurely removed from the web page before the scheduled end time. Therisk free interest rate, μ_(r), may equal the interest rate on atheoretically risk-free bond that matures at time T, the same time thatthe advertisement is scheduled to be removed from the web page. Thisinterest rate may be based on the interest rate of a low-riskinvestment, such as a U.S. Treasury bond, that is set to mature at timeT. The hazard rate, μ_(m), may be used to take into account theunexpected and premature removal of the advertisement from the web page.Raw data aggregator 201 may model this event as a random variable withan exponential distribution of rate μ_(m). A premature removal mayoccur, for example, when a web page is removed from the Internet. Insome embodiments, process control 203 may set the discount factor, μ, toequal:

μ=μ_(r)+μ_(m)

As an example of calculating the discount factor, process control 203may determine that the interest rate on a low-risk 30-day bond equals0.00005125 (0.005125%). Process control 203 may set μ_(r), the risk freeinterest rate, equal to 0.00005. Further, process control 203 may modelthe premature removal of an advertisement from a web page as anexponential distribution with a hazard rate, μ_(m), of 0.001.Accordingly, raw data aggregator may set the discount factor μ to equal0.00105. Process control 203 may transmit some or all of the calculatedvalues and the parsed data to verified data storage 205.

Target discovery module 207, may use the data in verified data storage205 to determine all web pages that have the same, or a similar, levelof performance for an advertising campaign. The level of performance maybe measured by some metric such as revenue per impression. Further,target discovery module 207 may be implemented by advertiser 101 or by athird party. The target web pages identified by discovery module 207 maybe different than the web pages for which advertiser 101 is currentlybidding.

To determine a list of target web pages, some embodiments of targetdiscovery module 207 may first decide on the web pages for which itdesires data. Target discovery module 207 may make this decision basedon one or more of performance metrics, demographic data, and statisticaldata of a web page. After target discovery module 207 identifies targetsthat have a desired level of performance for an advertising campaign, itmay then proceed to obtain information regarding the targets bytransmitting instructions to raw data aggregator 201. Raw dataaggregator 201, as discussed previously, may monitor and record datasignals involving the targets. Signals and data involving the target webpages may be transmitted from raw data aggregator 201 via processcontrol 203 to target discovery module 207. Target discovery module 207may pass the recorded signals and data to target evaluator 209.

Target evaluator 209 may accept the signals and data involving the setof targets from target discovery module 207 for analysis. Targetevaluator 209 may divide the targets into different sets according, forexample, to an evaluation of how well each target performs, or mayperform, in an advertising campaign. Moreover, target evaluator 209 mayhave a goal of identifying those targets that perform above a certainlevel in an advertising campaign, as measured by one or more metrics,such as, for example, the number of impressions, clicks, and/orconversions. Further, target evaluator 209 may have a goal of rankingeach target according to a specified metric and identifying a certainnumber of targets according to the rankings. For example, targetevaluator 209 may rank the targets according to the number of clicks andidentify the ten targets with the most clicks. After target evaluator209 has identified one or more target web pages, it may pass theidentified target web pages to target discovery module 207 which maystore the identified targets in inventory targets database 211 as targetinventory.

Campaign manager 213 may be used to achieve campaign goals 111 ofadvertiser 101. Campaign manager 213 may accept as input campaign goals111, verified data 205, and one or more target inventories frominventory targets database 211. In some embodiments, campaign manager213 may use the input data to calculate control information for bidcalculator 215. The control information may also include the preferenceand/or tolerance levels for an advertising campaign that advertiser 101transmitted as part of campaign goals 111. Campaign manager 213 mayfurther use the data in verified data storage 205 to set the value forone or more controls. By manipulating the control information, campaignmanager 213 may influence the bid prices determined by bid calculator215 for available advertising space. Campaign manager 213 may set thecontrol information based in part on the information transmitted withcampaign goals 111. After campaign manager 213 has determined theappropriate value for each control, it may then pass some or all of thecontrols, verified data, and target web pages to bid calculator 215.After bid calculator 215 determines the bid, it may transmit the bid tocampaign manager 213 which may then submit it as bid 113 to exchange105.

The processing of bid 113 by exchange 105 may be used as part of apositive feedback loop for optimizing bids 113 submitted to exchange105. For example, the processing of bids 113 by exchange 105 may provideadditional data 119 that can be transmitted to and collected by raw dataaggregator 201. After processing by process control 203, the additionaldata 119 may influence a later bid price calculated by bid calculator215 and submitted to exchange 105. Accordingly, using the additionaldata received from exchange 105, campaign optimizer 103 may manipulatethe controls passed to bid calculator 215 to optimize the value of bids113.

Bid calculator 215 may calculate bid values for placing advertisementsonto a target web page. In certain embodiments, the bid value forplacing an advertisement on a web page may be defined as the highestcharge that advertiser 101 is willing to pay for placing theadvertisement on a target web page. Bid calculator 215 may receive asinput from campaign manager 213 tolerance and/or preference informationof advertiser 101. Bid calculator 215 may also receive as input fromcampaign manager 213 verified data from verified data storage 205. Bidcalculator 215 may use some or all of the tolerance and/or preferenceindications, and the verified data to calculate a bid for the target.Bid calculator 215 may also use verified data from verified data storage205 to determine the bid. Bid calculator 205 may output a bid value tocampaign manager 213.

To compute the bid value, bid calculator 215 may first determine anequation to value the option of placing an advertisement on a target webpage. Bid calculator 215 may calculate the option value based on theshort-term expected profits that advertiser 101 expects to receive,given its current knowledge, from placing the advertisement on thetarget during advertising period [0, T]. Additionally or alternatively,bid calculator 215 may calculate the option value based on the learningvalue, the additional price that advertiser 101 is willing to pay toobtain a better estimate of its expected revenue if it maintains theadvertisement on the web page. Bid calculator 215 may base the learningvalue, in part, on the expected value of maintaining the advertisementafter the current learning period ends.

The value of maintaining the advertisement for a learning period thatbegins at time k may be referred to as the continuation value, C_(k), ofthe advertisement at time k. The continuation value at any time k is afunction of the future state of knowledge at time k. The continuationvalue of an advertisement for a learning period may include the expectedprofit of the advertisement for that learning period and an expectedvalue for the advertisement at the end of that learning period, wherethe expectations are a function of the state of knowledge at thebeginning of the learning period. Bid calculator 215 may determine theexpected profit by determining the expected revenue and then subtractingcosts. For example, the expected profit component of a continuationvalue for a learning period beginning at time k may equal:

P _(k)(ψ,c)=E(R _(k)(ψ))−c

where ψ is any of the possible states of knowledge at time k.

In certain embodiments, in addition to the expected profit component fora time period, the continuation value may also contain a future valuecomponent that represents the value of maintaining the advertisement atthe end of the learning period. When determining the future valuecomponent of the advertisement at the end of a learning period, bidcalculator 215 may estimate the option value of the advertisement as afunction of the possible states of knowledge occurring at the end ofthat learning period. Conditioned on the state of knowledge at thebeginning of a learning period, the bid calculator may then compute theexpectation of the option value over the possible states of knowledge atthe end of the learning period. In some embodiments, the expected valueof an advertisement after the current learning period may be discountedto a present day value when determining the option value at thebeginning of the current learning period. Accordingly, the future valuecomponent of the continuation value may be:

F _(k)(ψ,c)=e ^(−μ) E[V _(k+1)(ψ_(k+1) ,c)|ψ_(k)=ψ]

where ψ represents any of the possible states of knowledge at time k.

Bid calculator 215 may then sum the expected profit and future valuecomponents together to determine the continuation value of a learningperiod. Thus, bid calculator 215 may determine the continuation value ofa learning period beginning at time k as:

C _(k)(ψ,c)=P _(k)(ψ,c)+F _(k)(ψ,c)=(E(R(ψ))−c+e ^(−μ) E[V_(k+1)(ψ_(k+1) ,c)|ψ_(k)=ψ]

Moreover, because the expected value at the end of the last learningperiod equals zero, the continuation value for the last learning periodmay equal the expected profit for that time period:

C _(T-1)(ψ,c)=E(R(ψ))−c

for any state ψ.

After the continuation value, C_(k), at time k has been determined, bidcalculator 215 may determine the option value for any state at time k bycomparing the value of C_(k) to the option value of removing theadvertisement at time k. As an example, bid calculator 215 may set theoption value of a removed advertisement equal to zero. Accordingly, inthis example, bid calculator 215 may set the option value at any pointin time k to equal:

V _(k)(ψ,c)=max{0,C _(k)(ψ,c)}

FIGS. 3A-3B show an exemplary process 300 for determining a bid based onan option price consistent with an embodiment the present invention. Thedetermined bid represents an amount an advertiser is willing to pay forthe available inventory on a website. In the embodiment of FIGS. 3A-3B,to determine the bid, process 300 first values the option to place anadvertisement on the website. Process 300 then searches for a cost rateat which the option value is zero, and sets the bid equal to that costrate. Process 300 may be performed, for example, by bid calculator 215.

In FIG. 3A, a current option value is determined. The current optionvalue may take into account the ability to remove an advertisementbefore the end of advertising period [0, T]. For example, process 300may model the state of knowledge as a Markov decision process over afinite time period, [0, T] to determine the option value for maintainingan advertisement at any point in time based only upon the knowledge atthat time.

Process 300 begins by computing learning periods over time period [0, T](step 301). One or more points may exist within the advertising period[0, T] at which the advertisement may be removed from the target webpage. Accordingly, the time period [0, T] may be composed of one or moreperiods, called learning periods. The beginning of each learning periodmay correspond to one of the points at which campaign manager 213 mayremove the advertisement from the target web page. The first learningperiod may begin at time 0, while the last learning period may begin attime T−1. If the advertisement is removed from the web page, however,then bid calculator 215 may receive no further information regarding therevenue rate of the advertisement. Accordingly, when bid calculator 215receives no further information after an advertisement is removed, theremoval of an advertisement from the target web page may be consideredto be permanent when computing bid values.

When the advertisement may be permanently removed from the web page, bidcalculator 215 may determine a stopping time for the advertisement. Bidcalculator 215 may use the determined stopping time for an advertisementwhen calculating the option value of the advertisement. The stoppingtime represents a random variable that depends upon the expectations ofbid calculator 215, given its current knowledge, regarding the futurerevenue of maintaining the advertisement on the target web page.

Moreover, an optimal stopping time τ may exist at which the revenuesreceived from placing the advertisement on the target web page aremaximized. Some embodiments of bid calculator 215 may determine that theoptimal stopping time occurs when the option value V₀ satisfies thefollowing equation:

${V_{0}\left( {\psi_{0},c} \right)} = {\underset{\tau \in \Gamma}{\sup E}\left\lbrack {\sum\limits_{k = 0}^{\tau - 1}{e^{{- µ}k}\left( {{R\left( \psi_{k} \right)} - c} \right)}} \middle| \psi_{0} \right\rbrack}$

In this equation:

-   -   ψ_(k) is the knowledge of advertiser 101 at time instance k;    -   Γ is the set of admissible stopping times within the period [0,        T];    -   c is the fixed cost of placing the advertisement on the web page        in the given time period; and    -   R( ) is the random revenue as a function of the knowledge of        advertiser 101.

To solve the equation for the option value V₀, bid calculator 215 mayuse a series of comparisons between the values of maintaining andremoving the advertisement at the beginning of each learning period.Further, bid calculator 215 may use this series of comparisons to definethe stopping time in terms of a stopping condition. For example, thestopping time t may be defined as the time at which the value (V_(k)) ofmaintaining the advertisement on the web page at time t=k is less thanthe value of removing the advertisement.

Once the learning periods have been computed (step 301), process 300generates scenarios and transition probabilities for an estimatedrevenue rate for the set of learning periods (step 305). To generatescenarios of the estimates of revenue rates through the set of learningperiods, bid calculator 215 may represent the state of the knowledge attime t by ψ_(t)=(ř_(t),K_(t)), with ř being the estimate of the unknownrevenue rate and the K being the variance of this revenue rate estimate.When an advertisement is placed, the revenue rate per impression betweent and t+Δ may be assumed to be of the form:

y _(t+Δ) =r+v _(t,Δ)

with r being a true revenue rate for an impression and v_(t,Δ)representing measurement noise with mean zero and variance R/Δ.

Because r is unknown, scenarios are generated based on the currentestimate of the revenue rate ř_(t) and its variance K_(t). Accordingly,bid calculator 215 may model the mean and variance of the futureobserved revenue rate at time t+Δ, conditional on the knowledge state att, using the equations:

${E\left\lbrack y_{t + \Delta} \middle| \psi_{t} \right\rbrack} = {\overset{\smile}{r}}_{t}$${{Var}\left\lbrack y_{t + \Delta} \middle| \psi_{t} \right\rbrack} = {K_{t} + {\frac{R}{\Delta}.}}$

In these equations, ψ_(t)=[ř_(t),K_(t)] represents the state of theestimates at time t.

Once the estimated revenue rate scenarios are generated, process 300 maybegin determining a current option value by determining a continuationvalue for the final learning period, which may begin at time T−1 (steps305-306). For the final learning period, the continuation value equalsthe expected profit for that time period:

C _(T-1)(ψ,c)=E(R(ψ))−c

Process 300 then determines whether other learning periods remain (step307) and, if so, determines the continuation value for the priorlearning period (step 309). At any prior learning period, thecontinuation value may be found using the following equation:

C _(k)(ψ,c)=E(R(ψ))−c+e ^(−μ) E[V _(k+1)(ψ_(k+1) ,c)|ψ_(k)=ψ]

where κ=0, . . . , T−2. For learning periods prior to the final period,the continuation value also includes the expected value of the option atthe end of the time period, discounted to the beginning of the period.So, an option value for the prior learning period is determined (step311). The option value for a given state is determined using thefollowing equation-:

V _(T-1)(Ψ,c)=max{0,C _(T-1)(Ψ,c)}

As long as other learning periods remain (step 307, YES), process 300recursively determines continuation values and option values for eachprior learning period (steps 309, 311). For example, process 300 wouldcontinue to the time period beginning with T−2 and determine C_(T-2),the continuation value of the next to last learning period, usingV_(T-1) to determine the future value component of C_(T-1). As statedabove, the option value for the learning period beginning at time T−2may equal:

V _(T-2)(Ψ,c)=max{0,C _(T-2)(Ψ,c)}

Once the continuation and option values have been determined for eachlearning period, the current option value is set equal to the optionvalue based on the current cost rate estimate (step 313). This currentoption value is used to determine when an estimated cost rate should beset as a bid, as shown in FIG. 3A and discussed in greater detail below.

FIG. 4 shows an exemplary embodiment of a bid calculator consistent withan embodiment the present invention. Bid calculator 215 may perform someor all of the steps shown in FIGS. 3A-3B and may include learning periodmodule 405 and lattice module 410. The exemplary embodiment of bidcalculator 215 shown in FIG. 4 accepts as inputs campaign goals 111 fromadvertiser 101 and verified data 420 from verified data storage 205.

Learning period module 405 determines the length of each learning periodwithin the time period [0, T] for which an advertisement may be placedon a web page. Time period [0, T] may contain one learning period or mayinclude multiple learning periods. Learning period module 405 may acceptas inputs campaign goals 111 and verified data 420 from verified datastorage 205. Further, campaign goals 111 may include variance-reducingparameter S and variance-tolerance parameter γ. Variance-reducingparameter S may indicate a preference of advertiser 101 for reducing thevariance K of the revenue rate estimate as the advertisement remains ona web page. The reduction of K may be a linear, geometric, orexponential reduction of the value of K₀, the variance at time 0. Forexample, in some embodiments, advertiser 101 may indicate a preferencefor reducing the variance K so that the variance of each learning periodequals (1−δ) times the variance of the previous learning period.Accordingly, the variance K at the beginning of each learning periodstarting at time t=0 may be given by the geometric series Z: K₀, (1−δ)K₀, (1−δ)² K₀, etc. Variance tolerance parameter γ, may indicate thetolerance of advertiser 101 for the value of revenue rate variance K₀.Advertiser 101 that has a relatively high tolerance for the value ofrevenue rate variance K₀ may have a relatively higher value for variancetolerance parameter γ.

Learning period module 405 may determine the length of each learningperiod using the variance reducing parameter S. For example, bidcalculator 215 may seek to reduce the variance in the expected revenuerate per impression according to the geometric series Z. When using therevenue rate model y_(t+Δ)=r+v_(t,Δ) to determine the bid price, theKalman update equation may be used to determine that the error variancefor the next learning period equals:

$K_{t + \Delta} = \frac{K_{t}\frac{R}{\Delta}}{K_{t} + \frac{R}{\Delta}}$

Because the variance for each learning period equals to (1−δ) times thevariance of the previous learning period, bid calculator 215 may setK_(t+Δ)=(1−δ) K_(t). The length of a general learning period starting attime t is then given by:

$\Delta = \frac{\delta R}{\left( {1 - \delta} \right)K_{t}}$

Using this equation for the length of a learning period, learning periodmodule 405 may determine the number of learning periods during theperiod [0, T] based upon the duration of the advertising period [0, T]during which the advertisement can be placed on a web page and/or upon avariance tolerance parameter. When using the duration of the advertisingperiod, learning period module 405 may determine that the number oflearning periods equals:

$N_{T} = {\max\left\{ {\left\lbrack \frac{{\log(R)} - {\log\left( {{T \times K_{0}} + R} \right)}}{\log\left( {1 - \delta} \right)} \right\rbrack,1} \right\}}$

Additionally, learning period module 405 may use a variance toleranceparameter, γ, to set the number of learning periods within advertisingperiod [0, T]. For example, when the value of the estimated variance attime t is less than γ², learning period module 405 may determine thatthe value of learning is negligible. Accordingly, when using thevariance tolerance parameter to determine the number of learningperiods, learning period module 405 may set the number of learningperiods in period [0, T] to equal:

$N_{\gamma} = {{\max\left\{ {\left\lbrack \frac{{2{\log(\gamma)}} - {\log\left( K_{0} \right)}}{\log\left( {1 - \delta} \right)} \right\rbrack,0} \right\}} + 1}$

Learning period module 405 may compare learning period calculations todetermine the number of learning periods. For example, when the valuesof N_(T) and N_(γ) are calculated, learning period module 405 may choosethe minimum number of learning periods that are calculated according tothese different methods. Accordingly, learning period module 405 may setthe number of learning periods N to equal the minimum of N_(T) andN_(γ).

Bid calculator 215 may specify the variance of the revenue rate at thebeginning of each learning period by K₀ and K_(i)=(1−δ) K_(i−1), fori=1, . . . , N−1. Accordingly, bid calculator 215 may compute the lengthof the learning periods to equal:

${\Delta_{i} = {{\frac{\delta R}{\left( {1 - \delta} \right)K_{i}}{for}i} = 1}},\ldots,{N - 2}$

Finally, the length of the last learning period may be defined as:

$\Delta_{N - 1} = {T - {\sum\limits_{i = 0}^{N - 2}\Delta_{i}}}$

The times at which bid calculator 215 can decide to remove anadvertisement from a web page occur at:

t ₀=0;

t _(i) =t _(i−1)+Δ_(i−1), for i=1, . . . ,N−1.

If the advertisement is not removed at time t_(N-1), then it may beremoved at time T, the end of the advertising period. Learning periodmodule 405 may output series 460, T, which consists of decision timest_(i) for i=0, . . . , N−1, at which bid calculator 215 may decide tomaintain or remove an advertisement from a web page.

Continuing with FIG. 3B, to determine a bid price, process 300 estimatesa cost rate per impression c (step 317). Based on the cost rateestimate, process 300 determines a current option rate (step 319) byapplying the process described in FIG. 3A using lattice module 410.Lattice module 410 may accept verified data 420 from verified datastorage 205 and series T 460 as inputs.

FIG. 5 shows an exemplary embodiment of a lattice structure consistentwith the present invention. Lattice structure 500 may be used toconceptualize the process by which lattice module 410 may determine thecurrent option value based on cost rate estimate c. The x-axis 501provides a timeline for measuring time during the advertising period [0,T]. Time progresses on x-axis 501 from left to right, so that time t₀occurs before time t₁, time t₁ occurs before time t₂, etc. In latticestructure 500, time t₀ may represent the present time. Each subsequentmarked time on x-axis 501 represents the beginning of a learning periodwhen bid calculator 215 may decide to maintain or to remove anadvertisement from a web page.

The y-axis 505 enumerates nodes of the expected revenue rate, where eachnode corresponds to a state of the estimated revenue rate formaintaining an advertisement on a web page. Each state contains anestimate of the revenue rate and its variance. In some embodiments, thevalues on the y-axis may provide the expected revenue rate for a singlelearning period. For example, the y-axis value for node 512 mayrepresent an expected revenue rate for maintaining an advertisement on aweb page from time t₁ to time t₂ only.

Each of the nodes in lattice structure 500 represents an expectedrevenue rate for maintaining an advertisement on a web page for aspecific learning period. As shown in FIG. 5 , each learning periodafter the first learning period may have more than one expected revenuerates. For example, the learning period that begins at time t₁ may havethree different nodes 512, 514, and 516. Each of the different nodes mayrepresent different estimated expected revenues rates for a learningperiod. For example, the expected revenue rates for time t₁ associatedwith nodes 512, 514, and 516 may represent three different values. Thus,the expected revenue rate may be $0.0050 per impression for node 12,$0.0048 per impression for node 414, and $0.0046 for node 516.

Lattice structure 500 may also be used to represent relationshipsbetween nodes occurring at different learning periods. For example, thelines 552, 554, and 556 connecting node 510 to nodes 512, 514, and 516,respectively, may represent a relationship between node 510 and nodes512, 514, and 516. Lattice module 410 may represent these relationshipsas a probability that the expected revenue rate will move from a firstnode that occurs first in time to a second node that occurs later intime. For example, line 552 connects, and denotes a relationshipbetween, node 510 and node 512. Because node 510 occurs first in time,line 552 may represent the transition probability that the expectedrevenue rate for maintaining an advertisement will move from node 510 attime t₀ to node 512 at time t₁. If the expected revenue rate at node 510is $0.0048 per impression and the revenue rate at node 512 equals$0.0050 per impression, line 552 may represent the transitionprobability (e.g., 15%) that the revenue rate will increase from $0.0048per impression at time t₀ to $0.0050 per impression at time t₁. Thetransition probability may be defined as p_(i) ^(j,k)=Prob{ř_(i+1),ř_(i)^(j)}.

Lattice module 410 may calculate the expected revenue rates for eachnode and the probabilities connecting the nodes in lattice structure500. In some embodiments, lattice structure 500 may require that eachnode not in the last learning period be connected to three differentnodes in the next learning period. For example, as shown in FIG. 5 ,node 512 at time t₁ connects to nodes 524, 522, and 520 at time t₂.Further, the estimated revenue rates for the three nodes in the nextlearning period may be a step up from (i.e. greater than), equal to, anda step down from (i.e. less than) the estimated revenue rate in thecurrent learning period. For example, the estimated revenue rate at node524 may be greater than the estimated revenue rate at node 512, theestimated revenue rate at node 522 may be equal to the estimated revenuerate at node 512, while the estimated revenue rate at node 520 may beless than that at node 512. Similarly, nodes 524, 522, and 520 may eachbe connected to three different nodes in learning period t₃.

Lattice module 410 may establish a relationship between the values forthe revenue rate for each node and the probabilities connecting thenodes. For example, bid calculator 215 may calculate the value for therevenue rate of each node by requiring that the step up from a nodeequal the step down from the node. Accordingly, a value c may exist suchthat:

${\overset{\smile}{r}}_{i + 1}^{k} = \left\{ \begin{matrix}{{{\overset{\smile}{r}}_{i}^{j} + {\varepsilon{for}k}} = {j + 1}} \\{{{\overset{\smile}{r}}_{i}^{j}{for}k} = j} \\{{{\overset{\smile}{r}}_{i}^{j} - {\varepsilon{for}k}} = {j - 1}}\end{matrix} \right.$

Bid calculator 215 may use the value s to determine the values for theprobabilities connecting the nodes. Additionally, lattice module 410 maymanipulate the revenue rate model to calculate the probabilitiesconnecting the nodes in lattice structure 500. Corresponding to theobserved revenue rate model y_(t+Δ)=r+v_(t,Δ), the mean and variance ofthe distribution of the revenue rate estimate at node j at time t_(i)may be defined as ř_(i) ^(j) and K_(j), respectively. Using Kalmanupdate equations and the revenue rate model, the mean and variance ofthe estimated revenue rate during the next learning period beginning attime t_(i+1) may be determined as:

${E\left\lbrack {{\overset{\smile}{r}}_{i + 1}{❘\Psi_{i}^{j}}} \right\rbrack} = {\overset{\smile}{r}}_{i}^{j}$${{Var}\left\lbrack {{\overset{\smile}{r}}_{i + 1}{❘\Psi_{i}^{j}}} \right\rbrack} = {\sigma_{i + 1}^{2} = \frac{K_{i}^{2}}{K_{i} + \frac{R}{\Delta_{i}}}}$

In these equations, ψ_(i) ^(j) may be composed of the elements ř_(i)^(j) and K_(i). For example, ψ_(i) ^(j) may represent a state havingmean ř_(i) ^(j) and variance K_(i). The state for the initial node isdetermined by the inputs, i.e. ψ₀ ⁰=(ř, K₀). Lattice module 410 maydefine the probabilities associating nodes as a function of the firsttwo moments of the random variable described by the mean,E[ř_(i+1)|ψ_(i) ^(j)], and variance, Var[ř_(i+1)|ψ_(i) ^(j)], obtainedby the Kalman update equations. Matching the first moment requires thatp_(i) ^(j,j+1)=p_(i) ^(j,j−1). By matching the second moment, latticemodule 410 may require that:

$p_{i}^{j,k} = \left\{ \begin{matrix}{{{\frac{\sigma_{i + 1}^{2}}{2\varepsilon^{2}}{for}k} = {j + 1}},{j - 1}} \\{{1 - {\frac{\sigma_{i + 1}^{2}}{2\varepsilon^{2}}{for}k}} = j}\end{matrix} \right.$

To complete the transition probabilities, lattice module 410 may set thevalue of ε so that no negative probability values are calculated. Forexample, recognizing that σ_(i)>σ_(i+1), lattice module 410 may set thevalue of ε=σ₁ so that ε²=(σ₁)². Accordingly, lattice module 410determine that:

$\varepsilon^{2} = {\left( \sigma_{1} \right)^{2} = \frac{K_{0}^{2}}{K_{0} + \frac{R}{\Delta_{0}}}}$

As a result, lattice module 410 may use the value of ε to establish arelationship between the values for the revenue rate for each node andthe probabilities connecting the nodes.

After determining the value for each node and the transitionprobabilities, lattice module 410 may determine the option values foreach node. As discussed previously, the option value may consist of anexpected profit component and a future value component. Lattice module410 may begin by determining the option values for the nodes in the lastlearning period as shown by row 560 in lattice structure 500. Because nolearning periods occur after this learning period, the future valuecomponent for the nodes in the last learning period may equal zero.Thus, lattice module 410 may only need to calculate the expected profitsfor nodes in the last learning period. The expected profit for the lastlearning period may equal the expected revenue rate for the node minusthe cost rate of maintaining the advertisement, accumulated over thelast learning period. This discounted value of the expected profit maybe determined as:

$❘{{\int_{0}^{\Delta_{N - 1}}{{e^{- {\mu\tau}}\left( {{\overset{\smile}{r}}_{i}^{j} - c} \right)}d\tau}} = {\frac{1 - e^{- {\mu\Delta}_{N - 1}}}{\mu}\left( {{\overset{\smile}{r}}_{i}^{j} - c} \right)}}❘$

Thus, the option value for each node during this learning period may be:

$V_{N - 1}^{j} = {\frac{1 - e^{- {\mu\Delta}_{N - 1}}}{\mu}\max\left\{ {{{\overset{\smile}{r}}_{N - 1}^{j} - c},0} \right\}}$

After calculating the option value for each node in the last learningperiod, lattice module 410 may calculate the option value for thosenodes in the immediately preceding learning period that begins at timet_(N-2). The continuation value at this point may equal the estimatedprofit during the learning period at t_(N-2) as well as the discountedfuture value calculated for the end of this learning period. Latticemodule 410 may use the transition probabilities and the option valuescalculated for the nodes in the last learning period to calculate thecontinuation value for the learning period beginning at time t_(N-2).For example, lattice module 410 may calculate the continuation value foreach node in this learning period as:

$C_{N - 2}^{j} = {{\frac{1 - e^{- {\mu\Delta}_{N - 2}}}{\mu}\left( {{\overset{\smile}{r}}_{N - 2}^{j} - c} \right)} + {e^{- {\mu\Delta}_{N - 2}}{\sum\limits_{k = {j - l}}^{j + l}{p_{N - 2}^{j,k}V_{N - 1}^{k}}}}}$

Lattice module 410 may use the continuation value for each node in thelearning period beginning at time t_(N-2) to calculate the option valuefor each of these nodes.

FIG. 6 shows an exemplary embodiment of a portion of a lattice structureconsistent with an embodiment of the present invention and can be usedto illustrate the calculation of the option value for a node. In FIG. 6, node 601 occurs at time t_(N-2) and is associated with nodes 610, 612,and 614, each of which occur at t_(N-1), the beginning of the lastlearning period. The revenue rate at node 610 is a step up from therevenue rate of node 601, the revenue rate at node 612 equals therevenue rate of node 601, and the revenue rate of node 614 is a stepdown from the revenue rate of node 601. The transition probability 620represents the probability that the revenue rate at node 601 willtransition to the revenue rate at node 610. Transitions probabilities622 and 624 represent the same probabilities for nodes 612 and 614,respectively. In this exemplary embodiment, transition probability 620may equal transition probability 624.

Lattice module 410 may have placed values onto the nodes and transitionprobabilities in FIG. 6 . For example, lattice module 410 may have foundduring a previous calculation that both of the transition probabilities620 and 624 may equal, for example, 0.15. Accordingly, in this example,transition probability 622 equals 0.70. A previous calculation bylattice module 410 may have also have determined the option value foreach of nodes 610, 612, and 614. In this example, lattice module 410 mayhave calculated the discounted option value for node 610 to be $50, fornode 612 to be $45, and for node 614 to be $40. Finally, lattice modulemay have calculated the discounted total profit for node 601 during thelearning period at time t_(N-2) to equal $42. Using these values,lattice module 410 may calculate the continuation value for node 601 as:

C _(T-2) ^(j)=$42+(0.15×$50)+(0.70×$45)+(0.15×$40)=$87

Because the continuation value for node 601 is greater than zero, theoption value for node 601 equals $87.

Lattice module 410 may perform similar calculations for each node in alearning period. Lattice module 410 may also progress back thoughlattice structure 500 by calculating the continuation values and optionvalues for nodes in preceding learning periods. Using this method,lattice module 410 may calculate the option value V₀ ⁰ at time t₀. V₀ ⁰is the current option value given the current state of the revenue rateestimate and the supplied cost rate.

Continuing with FIG. 3B, process 300 determines when the current optionrate is zero (step 321) and then sets the bid equal to the cost rate cwhen that occurs. Given the relationship between Ψ₀ ⁰ and ř, V may bewritten as a function of K₀, c, and ř. V may further be written as afunction of the difference between ř and c. Finally, because c equals řplus the learning value, V may also be written as a function of thenegative learning value, −lv. Accordingly, the learning value may becomputed by setting V(−lv) equal to 0 and solving for the root of thisequation.

In some embodiments, a value for V may be computed using a bisectionmethod. For example, a value, x₀ may be found such that V(x₀) equalszero. The value of the learning value may then equal −x₀. As a firststep, the value of V(0) may be computed. If V(0) equals zero, then thelearning value also equals zero. If the value of V(0) does not equalzero, then the value of x_(u) may be set to zero. Next, the value of x₁is found where V(x₁) is less than zero. An initial guess for x₁ may beset at a negative number with a magnitude larger than the learningvalue. For example, in some embodiments, the value for x₁ may be set at−5√{square root over (K₀)} The value for x_(new) may be set to equal

$\frac{x_{1} + x_{u}}{2},$

and the value of V(x_(new)) may be computed. If the value of V(x_(new))is greater than zero, then the value of x_(u) may be set to x_(new);otherwise, the value of x₁ may be set to x_(new). If the absolute valueof x_(u) minus x₁ is less than a bisection tolerance parameter θ, thenthe learning value may be set to

$\frac{x_{1} + x_{u}}{2}.$

Otherwise, the process may repeat by finding a new value for x_(new)that equals

$\frac{x_{1} + x_{u}}{2}$

and computing a new value for V(x_(new)).

The following steps in a bi-sectional method may be used in someembodiments to find the learning value:

-   -   1. Set x_(u)=0.    -   2. Find a value of x₁ such that V(x₁)<0. For example, x₁ may be        set to equal −5√{square root over (K₀)}    -   3. Set

$x_{new} = \frac{x_{1} + x_{u}}{2}$

-   -    and compute V(x_(new)). If V(x_(new))>0, then set        x_(u)=x_(new). Otherwise, set x₁=x_(new).    -   4. If |x_(u)−x₁|<θ, then set the learning value equal to

$- {\frac{x_{1} + x_{u}}{2}.}$

-   -    Otherwise, return to step (3).

When the current option value equals zero (step 321, YES), the bid valueis set to the current cost rate estimate (step 323). The bid value maybe submitted to exchange 105. Exchange 105 may use the returned bidvalue Bo in filling requests 117 from publisher 107. Additionally, oralternatively, campaign manager 213 may submit a value based on the bidvalue to exchange 105. For example, campaign optimizer 103 may calculatea learning value that is then added to a revenue rate. The sum of therevenue rate and the learning value may then be submitted to exchange105. In some embodiments, the revenue rate used to compute the sum maybe different than the revenue rate used by campaign optimizer 103 tocalculate the learning value. Campaign optimizer 103 may use additionalor alternative equations to calculate a learning value.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

1-25. (canceled)
 26. A computer-implemented method for determiningelectronic content for display on one or more web pages, the methodcomprising: receiving, by a campaign optimizer over an electronicnetwork, campaign goal data and electronic content; identifying, basedon the campaign goal data, a target web page from the one or more webpages; receiving target web page data comprising data values of thetarget web page; providing a warning indication for abnormally behavingsignals of the data values; parsing, by the campaign optimizer, thetarget web page data to recursively determine one or more current optionvalues for a one or more learning periods, wherein determining the oneor more current option values comprises considering cell inventorylevels, a continuation value, a stop option value, and a current costrate estimate; setting a current option value of the one or more currentoption values to equal the stop option value based on the current costrate estimate; iteratively adjusting the current cost rate estimateuntil the stop option value equals zero; calculating a bid offer basedon determining that the stop current option value is zero and using alattice structure of expected revenue for maintaining display of theelectronic content on the target web page; transmitting the bid offer toa server processor associated with the target web page; and based onacceptance of the bid offer, displaying the electronic content on thetarget web page.
 27. The computer-implemented method of claim 26,further comprising calculating an expected value, wherein calculatingthe expected value includes: associating a set of expected values withthe learning period starting at an initial time; assigning a set oftransition probabilities to an initial expected value in the set ofexpected values, the set of transition probabilities defining arelationship between the initial expected value and one or more laterexpected values for a second learning period; and determining anexpected value based on at least one of the transition probabilities andat least one of a later expected revenue rates.
 28. Thecomputer-implemented method of claim 26, further comprising: calculatinga duration of the learning period as a function, at least in part, of ameasurement noise and an initial revenue-rate variance.
 29. Thecomputer-implemented method of claim 28, wherein calculating theduration of the learning period comprises calculating the duration as afunction, at least in part, of a variance-reducing parameter thatdetermines a reduction in the initial revenue-rate variance.
 30. Thecomputer-implemented method of claim 29, wherein the variance-reducingparameter is defined by a user.
 31. The computer-implemented method ofclaim 27, further comprising: creating the lattice structure, thelattice structure including a set of nodes, wherein an initial nodecorresponds to the initial expected value in the set of expected values.32. The computer-implemented method of claim 31, wherein a location ofthe initial node in the lattice structure is a function, at least inpart, of the initial expected values.
 33. The computer-implementedmethod of claim 31, wherein the set of transition probabilitiesassociated with the initial expected value is further associated withthe corresponding initial node.
 34. The computer-implemented method ofclaim 31, wherein the set of transition probabilities comprises: ahigher-revenue transition probability defining a relationship betweenthe initial node and a first later node in a second learning period; aneutral-revenue transition probability defining a relationship betweenthe initial node and a second later node in the second learning period;and a lower-revenue transition probability defining a relationshipbetween the initial node and a third later node in the second learningperiod.
 35. The computer-implemented method of claim 34, wherein thedifference in revenue between the first later node and second later nodeequals the difference in revenue between the second later node and thethird later node.
 36. The computer-implemented method of claim 34,wherein the higher-revenue transition probability equals thelower-revenue transition probability.
 37. The computer-implementedmethod of claim 26, further comprising: calculating a learning value asa function, at least in part, of the bid offer and the expected value ofthe learning period.
 38. A bid calculating system for determiningelectronic content for display on one or more web pages, the systemcomprising: a storage device that stores instructions for determiningthe electronic content; and a processing device that executes theinstructions to perform the following operations: receiving, by acampaign optimizer over an electronic network, campaign goal data andelectronic content; identifying, based on the campaign goal data, atarget web page from the one or more web pages; receiving target webpage data comprising data values of the target web page; providing awarning indication for abnormally behaving signals of the data values;parsing, by the campaign optimizer, the target web page data torecursively determine one or more current option values for a one ormore learning periods, wherein determining the one or more currentoption values comprises considering cell inventory levels, acontinuation value, a stop option value, and a current cost rateestimate; setting a current option value of the one or more currentoption values to equal the stop option value based on the current costrate estimate; iteratively adjusting the current cost rate estimateuntil the stop option value equals zero; calculating a bid offer basedon determining that the stop current option value is zero and using alattice structure of expected revenue for maintaining display of theelectronic content on the target web page; transmitting the bid offer toa server processor associated with the target web page; and based onacceptance of the bid offer, displaying the electronic content on thetarget web page.
 39. The bid calculating system of claim 38, wherein theprocessing device further executes the instructions to perform thefollowing operation: calculating a learning value as a function, atleast in part, of the bid offer and the expected value of the learningperiod.
 40. The bid calculating system of claim 38, wherein theprocessing device further executes the instructions to perform thefollowing operations: associating a set of expected values with thelearning period starting at an initial time; assigning a set oftransition probabilities to an initial expected revenue rate in the setof expected values, the set of transition probabilities defining arelationship between the initial expected value and one or more laterexpected values for a second learning period; and determining anexpected value based on at least one of the transition probabilities andat least one of the later expected values.
 41. The bid calculatingsystem of claim 38, wherein the processing device further executes theinstructions to perform the following operation: calculating a durationof the learning period as a function, at least in part, of a measurementnoise and an initial revenue-rate variance.
 42. The bid calculatingsystem of claim 41, wherein the processing device further executes theinstructions to perform the following operation: calculating theduration of the learning period as a function, at least in part, of avariance-reducing parameter that determines a reduction in the initialrevenue-rate variance.
 43. The bid calculating system of claim 42,wherein the variance-reducing parameter is defined by a user.
 44. Thebid calculating system of claim 40, wherein the processing devicefurther executes the instructions to perform the following operation:creating the lattice structure, the lattice structure including a set ofnodes, wherein an initial node corresponds to the initial expected valuein the set of expected values.
 45. A non-transitory computer-readablemedium storing instructions that, when executed by a processing device,cause the processing device to implement a method for determiningelectronic content for display on one or more web pages, the methodcomprising: receiving, by a campaign optimizer over an electronicnetwork, campaign goal data and electronic content, identifying, basedon the campaign goal data, a target web page from the one or more webpages; receiving target web page data comprising data values of thetarget web page; providing a warning indication for abnormally behavingsignals of the data values; parsing, by the campaign optimizer, thetarget web page data to recursively determine one or more current optionvalues for a one or more learning periods, wherein determining the oneor more current option values comprises considering cell inventorylevels, a continuation value, a stop option value, and a current costrate estimate; setting a current option value of the one or more currentoption values to equal the stop option value based on the current costrate estimate; iteratively adjusting the current cost rate estimateuntil the stop option value equals zero; calculating a bid offer basedon determining that the stop current option value is zero and using alattice structure of expected revenue for maintaining display of theelectronic content on the target web page; transmitting the bid offer toa server processor associated with the target web page; and based onacceptance of the bid offer, displaying the electronic content on thetarget web page.